Solve (b+4)^2-2(c-5)^2

$$( b + 4 ) ^ { 2 } - 2 ( c - 5 ) ^ { 2 }$$

Expand

$$b^{2}+8b-2c^{2}+20c-34$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(b+4\right)^{2}.

$$b^{2}+8b+16-2\left(c-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(c-5\right)^{2}.

$$b^{2}+8b+16-2\left(c^{2}-10c+25\right)$$

Use the distributive property to multiply -2 by c^{2}-10c+25.

$$b^{2}+8b+16-2c^{2}+20c-50$$

Subtract 50 from 16 to get -34.

$$b^{2}+8b-34-2c^{2}+20c$$

Evaluate

$$\left(b+4\right)^{2}-2\left(c-5\right)^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(b+4\right)^{2}.

$$b^{2}+8b+16-2\left(c-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(c-5\right)^{2}.

$$b^{2}+8b+16-2\left(c^{2}-10c+25\right)$$

Use the distributive property to multiply -2 by c^{2}-10c+25.

$$b^{2}+8b+16-2c^{2}+20c-50$$

Subtract 50 from 16 to get -34.

$$b^{2}+8b-34-2c^{2}+20c$$